Authors: | Tričković, Slobodan Stanković, Miomir |
Title: | A new approach to the orthogonality of the Laguerre and Hermite polynomials | Journal: | Integral Transforms and Special Functions | Volume: | 17 | Issue: | 9 | First page: | 661 | Last page: | 672 | Issue Date: | 1-Sep-2006 | Rank: | M23 | ISSN: | 1065-2469 | DOI: | 10.1080/10652460500421926 | Abstract: | This article draws on results from [Triković, S.B. and Stanković, M.S., 2003, On the orthogonality of classical orthogonal polynomials. Integral Transforms and Special Functions , 14(3), 271-280.], where we considered the orthogonality of rational functions W n ( s ) which are obtained as the images of the classical orthogonal polynomials under the Laplace transform. We proved in [Triković, S.B. and Stanković, M.S., 2003, On the orthogonality of classical orthogonal polynomials. International Transaction of Specific Function , 14(3), 271-280.] that the orthogonality relations of the Jacobi polynomials and the standard Laguerre polynomials L n ( x ) are induced by and are equivalent to the orthogonality of rational functions W n ( s ). In this article, we continue in the same manner by considering the generalized Laguerre polynomials and Hermite polynomials H n ( x ). In the last section, we analyze the zeros distribution of the Laplace transform images of the Legendre, Chebyshev, Laguerre and Hermite polynomials. |
Keywords: | Classical orthogonal polynomials | Laplace transform | Publisher: | Taylor & Francis |
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